Electronic Structure of the Lowest Triplet State of Flavin

Article pubs.acs.org/JPCA

Electronic Structure of the Lowest Triplet State of Flavin Mononucleotide Lydia Kammler† and Maurice van Gastel*,‡ †

Institut für Physikalische und Theoretische Chemie, Rheinische Friedrich-Wilhelms-Universität Bonn, Wegelerstrasse 12, 53115, Bonn, Germany ‡ Max-Planck-Institut für Chemische Energiekonversion, Stiftstrasse 34-36, 45470 Muelheim an der Ruhr, Germany S Supporting Information *

ABSTRACT: The electronic structure of flavin mononucleotide (FMN), an organic cofactor that plays a role in many important enzymatic reactions, has been investigated by electron paramagnetic resonance (EPR) spectroscopy, optical spectroscopy, and quantum chemistry. In particular, the triplet state of FMN, which is paramagnetic (total spin S = 1), allows an investigation of the zero field splitting parameters D and E, which are directly related to the two singly occupied molecular orbitals. Triplet EPR spectra and optical absorption spectra at different pH values in combination with time dependent density functional theory (TDDFT) reveal that the highest occupied orbital (HOMO) and lowest unoccupied orbital (LUMO) of FMN are largely unaffected by changes in the protonation state of FMN. Rather, the orbital structure of the lower lying doubly occupied orbitals changes dramatically. Additional EPR experiments have been carried out in the presence of AgNO3, which allows the formation of an Ag−FMN triplet state with different zero field splitting parameters and population and depopulation rates. Addition of AgNO3 only induces small changes in the optical spectrum, indicating that the Ag+ ion only contributes to the zero field splitting by second order spin−orbit coupling and leaves the orbital structure unaffected. By a combination of the three employed methods, the observed bands in the UV/vis spectra of FMN at different pH values are assigned to electronic transitions.

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INTRODUCTION Electron paramagnetic resonance (EPR) spectroscopy in combination with quantum chemical calculations, in particular density functional theory (DFT), is a powerful tool to study the electronic structure of paramagnetic molecules.1−3 Especially when applied to catalytically active molecules in catalysis or to organic or inorganic cofactors in enzymes, information obtained about their redox state or protonation state or changes thereof may provide information about the catalytic cycle itself. Moreover, if a redox reaction involves electron transfer with concomitant creation and/or annihilation of radicals and radical pairs, EPR spectroscopy can serve as an analytical tool to study dynamic processes up to the nanosecond time scale. 4−6 In favorable cases, pulsed electron−electron double resonance (pELDOR) spectroscopy may be used to directly measure the effective distance between the unpaired electrons.4,7 Though many studies by continuous wave and modern pulsed EPR spectroscopy exist in which the paramagnetic states are present as stable intermediates, an even larger group of molecules is not paramagnetic when they are functionally active. For organic chromophores, information about the electronic structure and catalytic cycle can still be obtained by EPR spectroscopy, if the molecule can be excited to a triplet state.8−22 Triplet states (S = 1) contain two unpaired electrons © 2012 American Chemical Society

and are therefore paramagnetic. The triplet state is usually reached upon promotion of an electron from a doubly occupied orbital into an empty orbital by excitation with light. Since the two unpaired electrons do not occupy the same orbital anymore, the spin of one of them may flip owing to spin− orbit coupling (SOC), thus generating the triplet state.23,24 This mechanism of triplet formation is called intersystem crossing (ISC). EPR studies of triplet states are much less common than those of radicals, for the obvious reason that the radical species concern ground states of molecules, whereas triplet states are metastable and typically have lifetimes in the microsecond range. The lifetimes of the three magnetic sublevels furthermore depend on spin−orbit coupling, and because spin−orbit coupling is a spin-selective interaction, the lifetimes are usually different. Often, the magnetic sublevel that attains most population also decays most rapidly. The amplitude of the EPR signal in the triplet state depends on the population difference of the resonant sublevels. Large EPR signals are present if the triplet state is fully polarized, ideally with only one triplet sublevel containing all the population. Since Received: June 13, 2012 Revised: September 7, 2012 Published: September 24, 2012 10090

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intersystem crossing competes with fluorescence and radiationless decay of the excited singlet state, which typically occurs on a nanosecond time scale, the absolute population or yield of the triplet state may be increased if the spin−orbit coupling interaction is maximized. In this paper, we study the triplet state of flavin mononucleotide (FMN, see Figure 1), a functionally relevant

whose exact wavelength slightly depends on the pH value and temperature. Under acidic conditions, all bands come together and give rise to one large absorption at about 400 nm.47 TDDFT studies for oxidized and reduced lumiflavin have provided first insights into the orbital structure.50,51 Both calculations indicate that the bands at 375 and 450 nm can be classified as π → π* transitions.51 Very recent studies using TDDFT in combination with QM/MM methodology confirm that the inclusion of environmental effects is crucial in order to reproduce the experimental spectra,52 as was also reported in the ab initio study of a large model for a flavin-bound protein.46 To the best of our knowledge, the pH dependence of the optical spectra has not been addressed yet by quantum chemical methods. For a detailed comparison of the electronic structure of the FMN cofactor from calculations with experimental data in solution and bound to the protein, information, e.g., by electron nuclear double resonance (ENDOR) spectroscopy of the photoexcited triplet state, is required. This information is not yet available for FMN in frozen solution. One reason for the lack of such studies is the low spin polarization of the excited triplet state and an exceptionally long lifetime of one of the triplet sublevels of 100 ms, making measurements very timeconsuming.18,53,54 In a pioneering study by Weber and Bittl with modern EPR spectroscopy, the triplet state of FMN has been reinvestigated.18 In this study, spin polarized triplet signals have been observed, albeit with low polarization. The magnetic interaction between the two triplet electrons, called zero field splitting (ZFS), and the decay kinetics of the triplet sublevels were found to depend on the protonation state of FMN. Three protonation states have been observed, in which the slowest decay was observed for the neutral FMN species.18 Especially the presence of a lifetime of 100 ms is indicative of a small SOC matrix element between the triplet state and the singlet ground state. In this study, we have successfully enhanced the intersystem crossing and concomitantly decreased the triplet lifetimes by increasing the spin−orbit coupling interaction. This is accomplished by adding silver nitrate to the solution. Since spin−orbit coupling becomes rapidly larger for heavier atoms, the introduction of such atoms aims at (1) increasing the absolute triplet yield, since ISC more effectively competes with radiative and nonradiative decay of the singlet excited state; (2) decreasing the triplet lifetime to the microsecond range, such that it can be more conveniently measured; and (3) increasing the spin polarization of the triplet state. Indeed, in liquid solutions, Ag+, Tl+, Ni+, Co2+, Tb3+, Sm3+, and Dy3+ were all found to significantly enhance ISC of the organic chromophores and thus act as triplet sensitizers.55−58 For FMN, the binding of heavy atoms and in particular the concomitant fluorescence quenching is known as well.59−62 In a frozen solution of FMN and the highly soluble AgNO3 , an enhancement is also reached, though at the expense of a high concentration of added AgNO3. The observed polarization pattern indeed changes significantly as well as the triplet lifetimes, though the amplitude of the signal still remains too low for ENDOR measurements.

Figure 1. Structure and IUPAC numbering scheme of neutral flavin mononucleotide (FMN).

molecule that acts as a cofactor in many enzymes that catalyze a wide variety of important biological processes.25−30 As examples, flavoproteins are active in DNA repair (photolyases). They also act as blue light photoreceptors related to the directional growth of plants (phototropins), and they are associated with the migration of birds or with the circadian or seasonal clock in plants (cryptochromes), where they trigger for example flowering or growing of new leaves. Additionally, they are involved in the emission of light in bacterial bioluminescence (luciferases). A more complete overview of classes of flavoenzymes is given elsewhere.28,30 Some classes of enzymes, e.g., the photolyases, have been shown to be radical enzymes.28 Though these classes are amenable to investigations by EPR spectroscopy, flavin radicals in proteins have only been scarcely studied with the aim of investigating their electronic structures when bound to the enzymes.31−41 For photolyases, the catalytic mechanism involves radical intermediates.42 The singly occupied molecular orbital has been calculated by DFT methodology, and calculated magnetic hyperfine coupling constants were shown to be in good agreement with experiment. Also, hydrogen bonding interactions to FMN are able to significantly influence the spin density distribution.42 For lumiflavin and isoflavin, time dependent density functional theory (TDDFT) calculations have been reported in which experimentally observed optical transitions have been calculated. The results agree well with experiment, and also the highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO) are reported.43 Quantum mechanical/molecular mechanical (QM/ MM) studies of flavins in proteins have been reported as well, where more of the environment has been included.44,45 Even a recent ab initio study of flavin in a large protein environment, performed with the small STO-3G to offset the computation time owing to the large model, gives rise to HOMO and LUMO surprisingly similar to DFT calculations with a larger basis set.46 The electronic transitions of FMN in solution at different pH values are well-known.47−49 At neutral and high pH values, two characteristic bands are present at about 375 and 450 nm,

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MATERIALS AND METHODS Sample Preparation. Flavin mononucleotide (FMN, 85% purity) was purchased from Fluka. Dry FMN was dissolved in deionized H2O or D2O (Deutero, ≥99%). Triplet EPR measurements were performed on samples with end concen10091

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trations of 1 and 10 mM, and UV/vis measurements were performed on samples with an end concentration of 0.1 mM. In addition, the solutions for EPR measurements contained 50% (v/v) glycerol or D-glycerol (Cambridge Isotope Laboratories, ≥98% purity) in order to obtain an optically transparent frozen solution. In measurements at low and high pH values, 37% HCl or 5 M NaOH solution was used. For experiments in D2O 35% DCl (Aldrich) and 5 M NaOD (Aldrich) was used. AgNO3 was added at neutral pH to a final concentration of 10 M. All samples were subsequently transferred to a Q-band EPR tube (diameter 2 mm) and were initially frozen at −20 °C and subsequently rapidly frozen and stored in liquid nitrogen. Measurements. UV/vis spectra have been recorded on a Beckman DU-64 UV/vis spectrometer at room temperature and with a concentration of 0.1 mM FMN. Pulsed EPR measurements were carried out on a Bruker Elexsys E580 FT EPR spectrometer with a Q-band EPR/ENDOR resonator and an Oxford CF935 helium gas flow cryostat at 30 K. For the electron spin echo (ESE) detected EPR experiments, a Hahn echo pulse sequence with pulses of 30 and 60 ns and a separation in time of 600 ns was used. Laser excitation was achieved by means of a Continuum Surelite II laser pumping an OPO Plus (OPO, optical parametric oscillator) laser. Light with a wavelength of 450 nm was used to excite the sample with an energy of 10 mJ/pulse. The repetition rate of the laser was 10 Hz. Calculations. DFT calculations have been performed with the ORCA program package. The model for FMN includes the complete molecule given in Figure 1. In order to mimic acidic conditions, the chromophore was protonated at position 1. For alkaline conditions, the chromophore was deprotonated at position 3 and the model was extended with a Na+ counterion. All calculations employ the TZVP basis set63 and the B3LYP functional.64,65 The spin−spin part of the ZFS has been calculated with a wave function obtained from a spin-restricted open shell calculation (ROKS), since it is known that the spin contaminationeven if smallinherent to unrestricted DFT formalism gives rise to ZFS parameters of mediocre quality.66 Since the goal of the theoretical investigation is to obtain chemical and physical insight into the orbital structure, the part of the ZFS resulting from spin polarization has been calculated manually according to a physically transparent formalism described elsewhere22 in analogy to the widely used McConnell theory for hyperfine interactions.67 In order to model the binding of silver, the geometry was augmented with an Ag+ ion bound trigonally to the oxygen atom at position 4, to the nitrogen atom at position 5, and to an additional water molecule.60,61 Additionally, the effect of the solvent was investigated for the deprotonated chromophore without the sodium ion and with inclusion of one or two additional water molecules and the COSMO model for solvation, using a dielectric constant of 80. These results are given in the Supporting Information. All models have been fully geometry optimized. In the ground state, the highest occupied molecular orbital (HOMO) is doubly occupied and the lowest unoccupied molecular orbital (LUMO) is empty. For the lowest triplet state both harbor one electron and are called singly occupied molecular orbitals (SOMOs). We will keep referring to these orbitals as HOMO and LUMO to indicate the HOMO is lower in energy than the LUMO. For the model, which includes Ag+, the contribution of spin−orbit coupling at Ag+ to the ZFS has been estimated manually by calculating the matrix elements

D⃗ ⃗ =

ζ2 ⟨n|L⃗|k⟩⟨k|L⃗|n⟩ En − Ek

(1)

where |n⟩ represents the Ag part of the wave function of the lowest triplet state and |k⟩ is the first excited triplet state, obtained by promotion of an electron from the HOMO − 1 to the HOMO. The HOMO contains 0.30% dxz character at Ag and the HOMO − 1 contains 0.67% dx2−y2 and 0.23% dxy character at Ag (Löwdin spin populations). The energy difference En − Ek is taken equal to the difference in orbital energies of the HOMO − 1 and the HOMO from the ROKS calculation, −17 650 cm−1. The spin−orbit coupling parameter ζ for silver amounts to 0.27 eV (2194 cm−1).68 After subtracting the trace, the Dzz element amounts to +24 × 10−4 cm−1, giving rise to a contribution by spin−orbit coupling equal to Dsoc = (3/2)Dzz = +36 × 10−4 cm−1 . The population of the triplet y level is expected to become much lower, since the contribution by spin−orbit coupling to the ZFS is largest along the y direction, whose orbital angular momentum operator connects the dxz orbital and the dx2−y2 orbital. No symmetry constraints were imposed on the molecule in any calculation. The g values have been calculated with a spinunrestricted formalism. Calculations of the electronic transitions were performed with TDDFT, a spin-restricted formalism, and the B3LYP functional, since Neiss et al. have shown that this method produces reasonably accurate results for uracil and lumiflavin.50

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RESULTS AND DISCUSSION UV/Vis Spectra. The UV/vis spectra of FMN at low, neutral, and high pH values and in deuterated solution are shown in Figure 2. At neutral and high pH values, two bands

Figure 2. UV/vis spectra (T = 296 K) of (a) 0.1 mM FMN in H2O, 37% HCl, and 5 M NaOH, respectively, and (b) 0.1 mM FMN in D2O, 37% DCl, and NaOD, respectively.

are present. The absorption maxima occur at 355 and 450 nm at high pH, and at 375 and 445 nm at neutral pH. The separation of these bands is largest at high pH and becomes smaller at neutral pH. The band at 450 nm additionally comprises two electronic transitions and displays a poorly resolved shoulder at 480 nm. At low pH, all bands seem to have come together and one unstructured band of doubled amplitude with an absorption maximum at 397 nm remains. In D2O the spectra are approximately the same as in H2O, and although the integrated absorptions agree well with those in H2O, the band at 450 nm at high pH and the one at 397 nm at low pH are less intense and broader than in H2O. The observed pH dependence is very similar to that observed by Beinert, 10092

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Nakamura, and Drössler for riboflavin.47−49 Interestingly, at acidic conditions, the remaining absorption at 400 nm is more narrow and intense in the case of FMN as compared to riboflavin. UV/vis spectra at neutral pH in the presence of AgNO3 are given in Figure 3. With the addition of AgNO3, the color of the

D2O recorded at the Q-band (34 GHz) and at 10 K are shown in Figure 4. Without AgNO3, the EPR spectra show a

Figure 3. UV/vis spectra (T = 296 K) of 0.1 mM FMN with the addition of 1 M AgNO3 and AgNO3 in excess respectively in (a) H2O and (b) D2O.

flavin becomes initially more reddish, but at concentration of 10 M AgNO3, the color becomes yellow again, with a bathochromic shift of the main absorption bands of 12 nm (375 nm) and 20 nm (445 nm), respectively, with respect to FMN at neutral pH. Interestingly, the absorption at 465 nm at 1 M AgNO3 in deuterated solvent is more red shifted, broader, and lower in intensity than the corresponding band in H2O. The presence of a band at longer wavelength than 500 nm upon addition of AgNO3 has been observed before. It has been extensively studied by Baarda and Metzler.61 They assign the band at 520 nm to complex formation and attribute the red color to an Ag−FMN adduct containing one or possibly two Ag+ ions bound to FMN. Centrifugation experiments with varying incubation times led to the conclusion that the redshifted absorption derives from Ag−FMN complexes with a high degree of polymerization.61 Under excess of AgNO3 as used here, the observation of a yellow color suggests that monomeric Ag−FMN complexes may be present. This is further inferred from the observation that the UV/vis spectra largely resemble that of FMN without AgNO3, whereas the polymerized complex displays an absorption maximum at 400 nm.61 Given that the red complex resembles the absorption spectrum of an FMN radical, the formation of a diradical Ag2+− FMN complex was suggested.60 EPR measurements, however, have not been able to confirm the existence of such a species at large AgNO3 concentrations. Bamberg and Hemmerich furthermore deduced that the bathochromic shift in the UV/ vis spectra of the flavin is not restricted to the presence of silver salts but is also characteristic for copper(I) and mercury ions or basically all d10 ions with a small energy difference between d9s1 and d10 electronic configurations.60 They attributed the redshifted complex to being a chelated trigonal complex in which the metal binds to N5, the neighboring keto-oxygen atom, and one solvent molecule. EPR Spectra and Simulations. In order to gain further insight into the electronic structure of FMN at different pH values or in the presence of an excess of AgNO3, ESE detected EPR spectra of the photoinduced triplet states of FMN have been recorded. The spectra with and without AgNO3 in H2O or

Figure 4. Q-Band ESE detected triplet EPR spectra at pH 7 and excited at 450 nm of (a) 1 mM FMN in H2O, (b) 1 mM FMN and 10 M AgNO3 in H2O, (c) 1 mM FMN in D2O, and (d) 1 mM FMN and 10 M AgNO3 in D2O. Simulations are included in the figure. Experimental conditions: T = 30 K; Hahn echo pulse sequence, 30 ns−400 ns−60 ns; microwave frequency 33.260 GHz. The canonical orientations for which molecules in the frozen solution oriented with their X, Y, or Z principal axis of the D tensor parallel to the magnetic field are included in (b).

polarization pattern characterized as EEEAAA (E = emissive, A = absorptive). The pattern changes upon addition of an excess of AgNO3 to EAEAEA. In all, the widths of the spectra with and without AgNO3 are similar. The zero field splitting parameters D and E, determined by simulation, are slightly larger when silver nitrate is present. The D and E parameters are furthermore similar to those observed by Weber and Bittl18 and are characteristic for an organic triplet state with essentially no spin density at silver. The triplet EPR spectra of FMN at different pH values show the same polarization pattern EEEAAA irrespective of the excitation wavelength. The widths of the spectra remain the same upon exchange of H2O to D2O, indicating that the line width is not dominated by unresolved 1 H hyperfine interaction. The EPR spectra have been simulated by using the formalism developed by Dauw et al.69 In this formalism, each zero field sublevel (Tx, Ty, Tz) is assigned a fractional population (px, py, pz) with px + py + pz = 1. An orientational average is performed over all possible orientations of the molecule in frozen solution, and for each orientation, the spin Hamiltonian H = μB B⃗ ·g ⃗ ⃗ ·S ⃗ ̂ + S ⃗ ·̂ D⃗ ⃗ ·S ⃗ ̂ 10093

(2)

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is diagonalized using the principal axis system of D⃗ ⃗ as a reference. In eq 2, μB is the Bohr magneton, B⃗ is the magnetic field, g ⃗ ⃗ is the g tensor with principal values (gx, gy, gz), and D⃗ ⃗ is the traceless zero field splitting tensor with principal values (−(1/3)D + E, −(1/3)D − E, (2/3)D). For each orientation, the population of the magnetic sublevels |MS⟩ (MS = 1, 0, −1) is given by pM = S

∑

|CiMS|2 pi

(3)

i=x ,y,z

where the coefficients CiMS are the eigenvectors of H. All spectra can be well simulated by using the parameters given in Table 1. Figure 5. Q-Band ESE detected triplet EPR spectra of 10 mM FMN in (a) 37% HCl and (b) 5 M NaOH, excited at 450 nm. The signals marked with asterisks derive from photogenerated radicals. Experimental conditions: T = 30 K; Hahn echo pulse sequence, 30 ns−400 ns−60 ns; microwave frequency 33.260 GHz. Simulations give rise to the following D values: D = 603 × 10−4 cm−1; D = 541 × 10−4 cm−1.

Table 1. ZFS Parameters D and E [10−4 cm−1], Populations of the Zero Field Triplet Sublevels px, py, and pz for the Triplet States of FMN and FMN with AgNO3 at pH 7, As Obtained from Simulationsa D E px py pz gx gy gz

FMN

FMN + AgNO3

535 167 0.5 0.4 0.0 2.0050 2.0037 2.0023

579 178 1.0 0.0 0.0 2.0023 2.0023 2.0023

DFT Calculations. DFT calculations have been performed on model systems that mimic FMN at acidic (FMN cation), neutral (neutral FMN) and alkaline (FMN anion) conditions. The HOMOs and LUMOs are shown in Figure 6. For all

a

The line width was 2.5 mT; a hyperfine interaction Azz of 100 MHz is included to take into account the anisotropy of the line width.

However, in order to reproduce the experimentally observed anisotropy of the line width, which is larger at the edges of the spectrum than in the center, an additional effective hyperfine coupling constant of 100 MHz has been included in the simulation for the Z canonical orientation. One discrepancy between experiment and simulation concerns the line shape at the X canonical orientation (see Figure 4). Here, the intensity is more peak shaped in the experimental spectrum than in the simulation. The reason for this discrepancy is likely related to the fact that the excitation by laser light in principle does not allow electric dipole transitions in the propagation direction of the laser light, thus giving an additional constraint in the orientation selection. We decided not to include this constraint, since the large amount of scattering in the sample largely but not completely lifts this degeneracy. Strikingly, the widths of the spectra in HCl and in NaOH differ as shown in Figure 5. The width of the spectrum is smaller at high pH than at low pH. This leads to a smaller D parameter at high pH (D = 541 × 10−4 cm−1) than at low pH (D = 603 × 10−4 cm−1), indicating that the effective distance between the triplet electrons is largest at high pH. The change of the effective distance is a direct consequence of slightly changed frontier orbitals of the isoalloxazine moiety depending on the protonation state of the isoalloxazine moiety. If these values are compared to those recorded at the X-band by Kowalczyk (D = 565 × 10−4 cm−1 at high pH and D = 629 × 10−4 cm−1 at low pH),18 the values derived from the X-band spectra are systematically larger by about 25 × 10−4 cm−1 . The reason is hyperfine broadening of about 60 MHz (vide infra), to which the X-band spectra are much more sensitive than the Q-band spectra.

Figure 6. Calculated HOMOs (bottom) and LUMOs (top) for FMN under acidic (left), neutral (middle), and alkaline (right) conditions.

models, the frontier orbitals concern π orbitals of the isoalloxazine moiety. They correspond well to the ones calculated by Neiss and Saalfrank for 10-methylisoalloxazine,43 though a few differences are also present. In particular, the 2pz orbitals at carbon atoms C4a, C5a, C9a, and C10a contribute more to the HOMO of FMN than to that of 10methylisoalloxazine. For the LUMO, density is present at carbon atoms 2 and 7, whereas for 10-methylisoalloxazine, density at these atoms is negligible. For acidic and pH neutral conditions, the orbitals are largely unaffected by the protonation state of FMN. The only notable difference in the HOMO occurs at N1, where protonation leads to a stabilization of the local N1(2pz) orbital and a reduced contribution of this orbital in the HOMO. For alkaline conditions, deprotonation at N3 results in an FMN anion. Without inclusion of mechanisms to stabilize the negative charge, the HOMO and LUMO change drastically and become incompatible with experiment (see Supporting Information). As an alternative to inclusion of a sodium counterion, water molecules have been added and solvent effects have included by the COSMO model in order to 10094

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Table 3. Calculated ZFS Parameters D and E and g Values for FMN with and without AgNO3a

stabilize the negative charge (see Supporting Information). Only with explicit inclusion of two water molecules and inclusion of further solvation effects with COSMO was the frontier orbital structure as found for pH neutral conditions recovered. These findings confirm earlier observations that environmental effects have a large influence on the electronic structure of FMN,40,52 and that the simplest model seems to be one where the negative charge is explicitly stabilized by a sodium counterion. The electronic transitions calculated by the TDDFT formalism and the oscillator strengths are presented in Table 2. The electronic transitions observed at 467, 445, and 372 nm

D [10−4 cm−1] Ddir [10−4 cm−1] Dpol [10−4 cm−1] Dsoc [10−4 cm−1] E [10−4 cm−1] gx gy gz

FMN, pH 7

FMN + AgNO3

FMN, pH 0

FMN, pH 13

540 477 63 0 131 2.0059 2.0046 2.0022

564 442 86 36 111 2.0128 2.0047 2.0023

550 480 70 0 160 2.0046 2.0038 2.0022

579 493 86 0 138 2.0057 2.0047 2.0023

a

The ZFS parameter D is specified in terms of the contribution by the direct dipole−dipole interaction, the contribution by spin polarization, and by spin−orbit coupling.

Table 2. Experimental and Calculated Electronic Transitions [nm] and Oscillator Strengths of FMN under Acidic, Neutral, and Alkaline Conditions, and in the Presence of AgNO3 at pH 7 pH 7 exptl

calcd

467 (0.026) 445 (0.082)

485 430 381 375

372 (0.172)

(0.116) (0.143) (0.138) (0.116)

exptl

calcd 459 (0.042)

396 (0.267)

pH 13 exptl

the spin-down, β electron attains more density at the proton. This causes additional spin density and a negative isotropic hyperfine interaction at the proton, which is a well-known phenomenon that is well described by the McConnell equation.67 The second triplet electron then magnetically interacts with the additional σ spin density caused by the first electron and vice versa. The contribution to the ZFS by spin polarization may to be on the order of 20% of the total ZFS and therefore not negligible.22 For FMN, the calculated direct dipole−dipole interaction of the two triplet electrons amounts to 477 × 10−4 cm−1 and the contribution by spin polarization amounts to 63 × 10−4 cm−1. The second order contribution by SOC is negligible for light atoms such as carbon and nitrogen (